Calculator
Formula used
- Standard floor: ⌊x⌋ is the greatest integer ≤ x.
- Standard ceiling: ⌈x⌉ is the smallest integer ≥ x.
- Decimal places (p): floor(x·10^p)/10^p and ceil(x·10^p)/10^p.
- Step size (s): s·floor(x/s) and s·ceil(x/s), where s > 0.
- Gaps: x − floor and ceiling − x measure the distances to each bound.
How to use this calculator
- Enter one value or paste a list of values in the input box.
- Select a rounding base: Integer, Decimal places, or Step size.
- Set the related parameter, then choose display formatting options.
- Click Calculate to view results above this form instantly.
- Use the download buttons to export your current results.
Example data table
| Input | Base | Parameter | Floor | Ceiling |
|---|---|---|---|---|
| 3.1416 | Decimal places | 2 | 3.14 | 3.15 |
| -2.7 | Integer | — | -3 | -2 |
| 12.999 | Step size | 0.25 | 12.75 | 13.00 |
| 125 | Decimal places | -2 | 100 | 200 |
These examples show how bounds change with precision and step choices.
FAQs
1) What is the floor of a number?
The floor is the greatest integer that is less than or equal to the value. For 3.2 it is 3, and for -3.2 it is -4 because -4 is the next integer below.
2) What is the ceiling of a number?
The ceiling is the smallest integer that is greater than or equal to the value. For 3.2 it is 4, and for -3.2 it is -3 because -3 is the next integer above.
3) Why does floor behave differently for negative values?
Floor always moves toward negative infinity. That means it goes to the next lower integer on the number line. With negatives, the next lower integer has a smaller value, like -4 being lower than -3.
4) How do decimal places bounds work?
The calculator scales by 10^p, applies floor or ceiling, then rescales back. With p=2, 3.1416 becomes 314.16, bounds are 314 and 315, then results become 3.14 and 3.15.
5) What does step size mean?
Step size builds bounds on a grid of multiples. With a step of 0.25, values are bounded by the nearest lower and higher quarter steps. It is useful for pricing increments, measurement tolerances, and quantized signals.
6) What does “On base” indicate in the results?
It means the value already lies exactly on the chosen grid, so the floor and ceiling are identical. For example, 5 is already an integer, and 12.75 is already a multiple of 0.25.
7) Can I paste many numbers at once?
Yes. Paste a list separated by commas, spaces, or new lines. The tool will compute bounds for each value and show them in a table. You can then export the entire table as CSV or PDF.
8) Are results exact for very large decimals?
Results use floating‑point arithmetic, so extreme magnitudes or many decimal digits may introduce rounding noise. For sensitive work, keep inputs within practical ranges, use fewer decimal places, and verify with a high‑precision tool when needed.